Mean-velocity field predictions

The ability of MTEN calculations to predict accurately the mean velocity field and turbulence kinetic-energy distribution is demonstrated by Fig. 17 from Mellor and Herring s contribution to the Stanford conference. Their use of a fine computational mesh near the wall is reflected in their accurate prediction of the inner regions. 

FIGURE 10.8 Comparison of predicted mean velocity field with angle-averaged PIV data (impeller center plane) (from Ranade et al., 2001 b). (a) Radial mean velocity (b) Tangential mean velocity. 

Note that when solving the CFD transport equations, the mean velocity and turbulence state variables can be found independently from the mixture-fraction state variables. Likewise, when validating the CFD model predictions, the velocity and turbulence predictions can be measured in separate experiments (e.g., using particle-image velocimetry [PIV]) from the scalar field (e.g., using planar laser-induced fluorescence [PLIF]). 

Figure 12.4 The comparison of predicted mean temperature fields in long and short combustors at t = 14.9 ms (a), 22.1 (6), and 58.1 ms (c) after ignition behind a bluff body. Boundary condition at outlets is ABC of Eq. (12.19). Mean velocity at the inlet Uin = 10 m/s. Other conditions are po = 0.1 MPa, To = 293 K, fco = 0.06 J/kg, lo = 4 mm. A set of graphs below compares mean absolute velocity distributions in the different cross-sections (/ to VII) of both combustors (from left to right x = 0, 80, 100, 112, 135, 235, and 330 mm). Solid line — short combustor, dashed line — long combustor, j/max is the height of the corresponding cross-section of the combustor...

Now, consider a natural river, illustrated in Figure 9.3. There are many sources of vorticity in a natural river that are not related to bottom shear. Free-surface vortices are formed in front of and behind islands and at channel contractions and expansions. These could have a direct influence on reaeration coefficient, without the dampening effect of stream depth. The measurement of p and surface vorticity in a field stream remains a challenge that has not been adequately addressed. The mean values that are determined with field measurements are not appropriate. Most predictive equations for reaeration coefficient use an arithmetic mean velocity, depth, and slope over the entire reach of the measurement (Moog and Jirka, 1998). The process of measuring reaeration coefficient dictates that these reaches be long to insure the accuracy of K2. Flume measurements, however, have generally shown that K2 u /hor K2 (Thackston and Krenkel, 1969 ... 

In polymers, it is always observed that a packet of carriers spreads faster with time than predicted by Eq. (30). Thus, the spatial variance of the packet yields an apparent diffusivily that exceeds the zero-field diffusivity predicted by the Einstein relationship. Further, the pholocurrent transients frequently do not show a region in which the photocurrent is independent of time. As a result, inflection points, indicative of the arrival of the carrier packet at an electrode, can only be observed by plotting the time variance of the photocurrent in double logarithmic representation. The explanation of this behavior, as originally proposed by Scher and Lax (1972, 1973) and Scher and Montroll (1975), is that the carrier mean velocity decreases continuously and the packet spreads anomalously with time, if the time required to establish dynamic equilibrium exceeds the average transit time. Under these conditions, the transport is described as dispersive. There have been many models proposed to describe dispersive transport. Of these, the formalism of Scher and Montroll has been the most widely used. 

These models require information about mean velocity and the turbulence field within the stirred vessels. Computational flow models can be developed to provide such fluid dynamic information required by the reactor models. Although in principle, it is possible to solve the population balance model equations within the CFM framework, a simplified compartment-mixing model may be adequate to simulate an industrial reactor. In this approach, a CFD model is developed to establish the relationship between reactor hardware and the resulting fluid dynamics. This information is used by a relatively simple, compartment-mixing model coupled with a population balance model (Vivaldo-Lima et al., 1998). The approach is shown schematically in Fig. 9.2. Detailed polymerization kinetics can be included. Vivaldo-Lima et a/. (1998) have successfully used such an approach to predict particle size distribution (PSD) of the product polymer. Their two-compartment model was able to capture the bi-modal behavior observed in the experimental PSD data. After adequate validation, such a computational model can be used to optimize reactor configuration and operation to enhance reactor performance. 

We conclude that over the continuum scale the determining parameters are the wind speed Uh and turbulence initial parameters of the cloud/plume when it reaches the top of the canopy or, equivalently, the virtual source at the level of the canopy. Using suitable fast approximate models for the flow field over urban areas (e.g. RIMPUFF, FLOWSTAR), the variation of the mean velocity and turbulence above the canopy can be calculated. The FLOWSTAR code (Carruthers et al., 1988 [105]) has been extended to predict how (Uc) varies within the canopy. Dispersion downwind of the canopy can also be estimated using cloud/plume profiles, denoted by Gc,w,GA,w which are shown in Figures 2.20 and 2.22. 

Lane et al [49] did compare the performance of simulations with the SM and the MRF approach in predicting flow fields within a standard stirred tank equipped with a Rushton turbine. Reasonable agreement with experimental data in terms of mean velocities is obtained with both methods. Nevertheless, the MRF method provides a saving in computational time of about an order of magnitude. 

Prediction of the gas-phase mean and rms velocity fields and the distribution of the liquid axial mass fluxes as predicted by the simulation are in good agreement with the experimental data. Details of these comparisons are provided by Apte et al. [36]. The breakup model does not include coalescence effects. In addition, the effect of injecting different size distributions near the injection must be investigated to address sensitivity of the model parameters to flow conditions. Specifically, size distributions further away from the injector (in the intermediate and dilute regimes) may be influenced by these inlet conditions. 

ABSTRACT The mean flow features of two types of wall jets used often in hydraulic engineering are analyzed. They include the results of a plane jet and a three-dimensional wall jet. The required flow field was obtained from CFD simulations, the point source method and some limited experiments. These are compared with the available equations in vogue, which predict the growth of the jet, the decay of the maximum mean velocity and concentration of tracers. The variation of the wall shear stress along the flow is also analyzed. The CFD results for the distribution of the mean velocity and the tracer concentration exhibit self-similarity . However, the predicted growth rate of the jets differs from the available data. 

The purpose of this investigation is to find the flow features of the aforementioned jets from CFD simulations and establish their efficacy in predicting the mean flow field for which experimental results are available. For the plane and the three-dimensional wall jets, the simple point-source technique was also applied to predict the decay of the maximum velocity and the tracer concentration with the distance x. In the computations of the present study, GAMBIT ver 2.4 was used as the preprocessor and Fluent ver 6.3.26 as the processor and post processor. Based on the earlier experiences, the K-e realizable model was considered suitable for the computations. The efflux velocity was selected as 2.0 m/s and the slot height h = 0.01 m. The intensity of turbulence at the efflux section was considered as 1%. For finding the distribution of the tracers, the density of the particles was made equal to that of the ambient fluid. 

For the simulation to be completely successful, the turbulence field must be as accurately predicted as the velocity field. Where the simulations by Fokema et al. [19] used a tank geometry equivalent to the experimental conditions, the simulated and experimental values of the turbulent kinetic energy (k) showed reasonable agreement. The predicted energy dissipation rate (8) profiles immediately below the impeller were of the correct magnitude, but further away from the impeller, the predicted values of 8 decayed to only a fraction of the experimental values. This underprediction of the dissipation rate was also evident in mean values above the impeller. 

At this end, to demonstrate superiority of our classical algorithms, we show some sample results of our most recent FDF simulation of the Sandia/Sydney swirl burner [35]. This configuration is selected as it is one of the most challenging turbulent flames for prediction. Figure 3 shows the contours of the azimuthal velocity field as predicted by our FDF. The simulated results agree with experimental data better than any other classical methods currently available [36]. But the computational time requirements are excessive. As another example. Fig. 4 shows the contour of filtered temperature field for the symbolic Taylor-Green vortex flow as obtained via FDF coupled with a discontinuous Galerkin flow solver [37]. Quantum computation may potentially provide a much more efficient means for such simulations. 

---